integrate ((y^6/3)+y^3-(y^3/3)-y^2))dy from 1 to 2

@agent0smith

the answer is 87/14

Question

integrate ((y^6/3)+y^3-(y^3/3)-y^2))dy from 1 to 2

@agent0smith 

the answer is 87/14

abb0t · Answer

$$\int\limits \frac{y^6}{3}+y^3-\frac{y^3}{3}-y^2~dy$$

anonymous · Answer

youre soo pretty !!!!!!!!!!!!!!!!!!!!!!!!!!!

abb0t · Answer

You think I don't know what i am?

megannicole51 · Answer

thank you

anonymous · Answer

my pleasure!!!

abb0t · Answer

That's not the answer. I'm asking if that's the given integral.

megannicole51 · Answer

yes it is

megannicole51 · Answer

and yes it is

abb0t · Answer

$$\frac{1}{3}\int\limits y^6~dy + \int\limits y^3~dy - \frac{1}{3} \int\limits y^3~dy - \int\limits y^2~dy $$
then, evaluate the integrals, as you should normally would.
Then following the Fundamental Theorem of Calculus part II, where F(b)-F(a) 
Use that property to solve. Where $\sf \color{red}{b = 2}$, $\sf \color{limegreen}{a = 1}$

abb0t · Answer

For instance, the first integral, you would get $\sf \color{blue}{\frac{1}{21}y^7}$, now, you do $\sf \color{orange}{\frac{1}{21}[(2)^7-(1)^7]=}$....

megannicole51 · Answer

okay i got it now thank you so much

abb0t · Answer

You can finish the rest now, right?

megannicole51 · Answer

yup:)

megannicole51 · Answer

actually hold on...

so i got $$\frac{ y ^{7} }{ 21 }+\frac{ y ^{4} }{ 4 }-\frac{ y ^{4} }{ 12 }-\frac{ y ^{3} }{ 3 }$$

is that right so far?

anonymous · Answer

@abb0t

abb0t · Answer

Yes.

megannicole51 · Answer

jk i got it...it is right

megannicole51 · Answer

then you just plug in:) thank you

abb0t · Answer

Now you need to apply fundamental theorem of calculus and solve.

megannicole51 · Answer

yup got it:) thanks! sorry i doubted myself

agent0smith · Answer

Doubt yourself less, Meg :P

megannicole51 · Answer

hehe yeah yeah!

agent0smith · Answer

You're very smart! :)

abb0t · Answer

@agent0smith she's like 12. Stop.

agent0smith · Answer

She's a university student.

zarkon · Answer

For all you know 'she' could be a 400lb university custodian.  You can be what you want to be on the internet.

abb0t · Answer

Are you implying something there?

zarkon · Answer

I am an android.  I don't imply anything.

abb0t · Answer

I'm on to you.

anonymous · Answer

what ??????

zarkon · Answer

don't tell Dr. Soong.

anonymous · Answer

umm

megannicole51 · Answer

um excuse me but I'm 20 and that is my actual picture and i go to the university of colorado so no im not 12 or fat thank you very much

zarkon · Answer

Since no one lies on the internet I believe you ;)